Question: Evaluate the definite integral. $\int^{1}_{5}\big(-4x+1\big)\,dx = $
Answer: First, use the power rule: $\int^{1}_{5}\big(-4x+1\big) ~=~-2 x^2+x\Bigg|^{{1}}_{5}$ Second, plug in the limits of integration: $\big[-2\cdot{1}^2+{1}\big]-\big[-2\cdot{5}^2+{5}\big] = -1 +45 =44$. The answer: $\int^{1}_{5}\big(-4x+1\big) ~=~ 44$